A counter example to the Bueler's conjecture

A counterexample to Belgun-Moroianu conjecture

We construct an example of a closed manifold with a nonflat reducible locally metric connection such that it preserves a conformal structure and such that it is not the Levi-Civita connection of a Riemannian metric.

A counter-example to a recent version of the Penrose conjecture

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.

关于三维球上Escobar的Steklov猜想的一个初等反例

An elementary counterexample to Escobar's Steklov conjecture on the three-ball

本文构造了单位三维球上满足正Ricci曲率与严格凸边界条件的显式多项式度量形变，作为Escobar关于Steklov特征值下界猜想的反例，其证明可人工验证。

A C^2-smooth counterexample to the Hamiltonian Seifert conjecture in R^4

We give a detailed construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

双曲度量附近普通Fried猜想的反例

Counterexamples to the ordinary Fried conjecture near hyperbolic metrics

该研究借助LLM辅助构造三维双曲度量附近普通Fried猜想的反例，证明非循环酉线特征趋于平凡特征时，Ruelle ζ函数零点模与解析挠率平方的比值趋于0。